Related papers: Hyper-invariant tensor networks and holography
Random tensor networks are a powerful toy model for understanding the entanglement structure of holographic quantum gravity. However, unlike holographic quantum gravity, their entanglement spectra are flat. It has therefore been argued that…
Four lectures on holography and the AdS/CFT correspondence applied to condensed matter systems. The first lecture introduces the concept of a quantum phase transition. The second lecture discusses linear response theory and Ward identities.…
We demonstrate, in the context of quadratic fermion lattice models in one and two spatial dimensions, the potential of entanglement renormalization (ER) to define a proper real-space renormalization group transformation. Our results show,…
We have discussed the tensor-network representation of classical statistical or interacting quantum lattice models, and given a comprehensive introduction to the numerical methods we recently proposed for studying the tensor-network…
In the long-standing quest to reconcile gravity with quantum mechanics, profound connections have been unveiled between concepts traditionally pertaining to quantum information theory, such as entanglement, and constitutive features of…
Modeling the joint distribution of high-dimensional data is a central task in unsupervised machine learning. In recent years, many interests have been attracted to developing learning models based on tensor networks, which have the…
The study of low-dimensional quantum systems has proven to be a particularly fertile field for discovering novel types of quantum matter. When studied numerically, low-energy states of low-dimensional quantum systems are often approximated…
Interacting systems of anyons pose a unique challenge to condensed matter simulations due to their non-trivial exchange statistics. These systems are of great interest as they have the potential for robust universal quantum computation, but…
We propose a surface growth approach to reconstruct the bulk spacetime geometry, motivated by Huygens'principle of wave propagation. We first construct a tensor network corresponding to a special surface growth picture with spherical…
Quantum phase transitions between different topologically ordered phases exhibit rich structures and are generically challenging to study in microscopic lattice models. In this work, we propose a tensor-network solvable model that allows us…
In this article we present analytical results on the exact tensor network representations and correlation functions of the first examples of 2D ground states with quantum phase transitions between area law and extensive entanglement…
We propose a symmetric version of the multi-scale entanglement renormalization Ansatz (MERA) in two spatial dimensions (2D) and use this Ansatz to find an unknown ground state of a 2D quantum system. Results in the simple 2D quantum Ising…
The holographic duality (also known as AdS/CFT correspondence or gauge/gravity duality) postulates that strongly coupled quantum field theories can be described in a dual way in asymptotically Anti-de Sitter space. One of the cornerstones…
These are course notes for the 'Introduction to holography' Master level course at University of Cologne. The goal of the course is to give a pedogogical introduction to holography. Holography is a popular approach to quantum gravity, in…
While tensor networks have their traditional application in simulating quantum systems, in the recent decade they have gathered interest as machine learning models. We combine the experience from both fields and derive how quantum…
Tensor Networks are non-trivial representations of high-dimensional tensors, originally designed to describe quantum many-body systems. We show that Tensor Networks are ideal vehicles to connect quantum mechanical concepts to machine…
Leveraging the decomposability of the fast Fourier transform, I propose a new class of tensor network that is efficiently contractible and able to represent many-body systems with local entanglement that is greater than the area law.…
We present how the surface/state correspondence, conjectured in arXiv:1503.03542, works in the setup of AdS3/CFT2 by generalizing the formulation of cMERA. The boundary states in conformal field theories play a crucial role in our…
Tensor networks provide a powerful tool for studying many-body quantum systems, particularly making quantum simulations more efficient. In this article, we construct a tensor network representation of the spin network states, which…
Quantum many-body problem with exponentially large degrees of freedom can be reduced to a tractable computational form by neural network method \cite{CT}. The power of deep neural network (DNN) based on deep learning is clarified by mapping…